NEW HAVEN, Conn. — A man set his girlfriend on fire and also tried to douse her 12-year-old daughter after the girl accused him of inappropriately touching her, police said.

The girl managed to escape the flames Sunday morning and rescue her 3-month-old sister, police said. Neither girl was injured, but their 35-year-old mother was hospitalized in critical condition with burns on up to 40 percent of her body.

Howard Stewart, 50, of New Haven, was arraigned Monday on charges including first-degree arson, first-degree assault and attempted assault. He didn’t enter a plea and was held on $2 million bail. A telephone message left with his public defender wasn’t immediately returned.

The 12-year-old girl said she told her mother Saturday night that Stewart had inappropriately touched her and that she was scared of him, according to a police report. That led to an argument between the couple and her mother saying she would go to police.

The next morning, the girl woke up when she felt liquid being poured on her and then saw Stewart striking matches and tossing them toward her, police said. The girl ran from the room, but stopped when she saw a fire. Howard grabbed her, dragged her back to her room, threw her back on the bed, poured more liquid on her and then fled, police said.

The girl saw flames and then she noticed that her sister was still asleep. She grabbed the baby and fled to the first floor, where she found her mother naked and burned. The woman banged on the door of another apartment in the building; the tenants heard her screaming and called police.

The mother was in severe pain, but managed to tell police that Stewart burned her, according to the police report.

Stewart was arrested nearby. Police said they found him with several wooden match sticks in his pocket. He has prior domestic violence convictions in the 1990s, including assault, prosecutors said in court.

After his arrest, Stewart asked a police officer if his 3-month-old daughter was OK and asked, “Did she get hurt by the fire?,” according to police.

Police said Stewart told investigators: “Things just went too far you know, we were arguing about things.”

Stewart said he and his girlfriend had been arguing a lot lately – over bills, about him not working and about the older girl’s allegations, which he called “lies,” according to police.

“I couldn’t take it any more. She wouldn’t listen,” Stewart said, according to the report.